Rational numbers possess five fundamental properties: closure (adding, subtracting, multiplying, or dividing two rational numbers always yields a rational number), commutative (a + b = b + a and a × b = b × a), associative ((a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)), identity (0 for addition, 1 for multiplication), and inverse (additive inverse is -a, multiplicative inverse is 1/a). These properties are verified through examples such as adding -5/7 and 8/9 to get 11/63, and multiplying -10/11 by -8/33 to get 80/363.
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Deep Dive
8th Maths | Chapter 1 Exercise 1.3 Explained Step by Step | TN State Board | Janasruthi Ma'am
Added:Hello everyone.
Hi பசங்களா.
So, welcome to Vedantu channel, my colleague.
Hello.
So, பசங்களா எல்லாம் எப்படி இருக்கீங்க?
How was your school is going on?
You know, ஒருத்தர் கூட கமெண்ட் செக்ஷன்ல காணோம். எல்லாரும் எங்க போயிட்டீங்க?
ஏதோ சுத்திட்டே இருக்கு.
>> So come on can we start?
So regular students in the building So eight standard students daily weekly weekly Thursday Saturday in the live sections So Yep in the live section in the live continue or otherwise live section I'll be stopping eight standard So I'm saying that you want live section eight standard and getting live section meaning regular Yes. Hi Kritika.
Okay.
Okay. So Kritika student friends live section live section Okay.
fractions already fractions properties properties properties properties Hi everyone.
>> Hi everyone.
Yes.
Okay, hi Roshni. Yeah.
Okay.
1 2 3 5 Yeah. Five properties in the proper cupboard.
12 standard 12 standard chapter in the properties that chapter Yes.
So, 12 standard max math reading a part of Okay.
Yeah, that was a good angle.
Mother India mother wish you wanted to Yes. Another come on guys.
fire You do me kind of Put it on I don't know what to say right now. Yes.
mother to pay getting quarter I think I don't know what to do. I think I don't know. I think I don't know.
I don't know what to do. I don't know what to do.
I don't know what to do. I don't know what to do.
>> Sorry, I do not I do not do. Yeah, I do not do fun.
Okay, well.
Hi everyone. Yes.
Closure I'm doing about taking in a lot of you know what I'm saying love.
See in the class.
I don't know first in the last of one hour class.
So everyone.
I do not do I do not do what is I do not do means.
I do not do I do not do I do not do you know what I'm I do not do closure.
Closure.
I do not do I do not do I do not I do not do number.
I do not do I do not do number.
We are taking two rational number.
I do not do I do not do I do not do I do not do I do not do I do not I do not do or rational number rational number or fraction.
Okay, everyone.
Okay, well I do not do number I do not I do not do fraction I do not do I do not instead of taking any fraction.
Yes.
12 standard or equal Very good.
1/2 3/4 1/2 and 1/2 only 4 equal 3/4 3/4 only 4 equal You will represent them out there.
Correct or not?
You enter the end of fraction of any number equal. Put it on or I So the other way You think of it.
1/2 3/4 1/9 equal So you can fraction might be getting equal. So you can be in the end of fraction I don't know if you don't agree.
What do you think of Do you have a number? So you can have a number equal.
You can be in the end of number equal.
7c class of equal or equal Done. I don't know if you don't agree. You can be in the end of any fraction You can have a number equal. You can be in the end of fraction You can be in the end of number You can be in the end of number You can be in the You can be in the end of number You can be in the end of number You can be in the end of fraction You can be in the end of number >> I'm going to race in a number.
So I'm going to let it go down.
What example can I mean with an example? So tell me now.
Yeah, that fraction back there.
Be that fraction.
Anyone you have one? You have even with the money on it. Yeah, you have that fraction. Any fraction that was in So English is learning.
It was going to turn on the fraction to become a building.
Yes. A in the fraction. Be in the fraction. You have the fraction of a plan.
Yeah, everyone.
10th year for mom start planning.
3 by 4 okay. 3 by 4. Be that so long.
Book up so long book of this so long I will see okay. What? Custom book like that is so long and I Any other you have so long be that fraction. You have so long negative so long positive so long on this you have that so long.
I'm going to book like that we know what you mean 6 by 4 okay.
6 by 4.
Say. You have to be there at the end of that.
3 plus 6 by 4 and I would just 9 by 4 and I would not. What fraction that is?
Yes.
So you can pay that closure. random rational number edited very good random rational number random rational number but not anything wrong I think my dear I think what a rational number that answer I want to know and the closure property about Okay. in the rational number Okay.
community commutative commutative but I might matter but I might uh but I might fun but Okay, I don't know. Even in a moment I mean getting that but I might not know the sharing. I don't know sharing I've been getting you know random rational number I don't know but not a plus b a plus b I don't know but not in the answer I want to know I don't know but I might be putting b plus a I don't know but I might be putting the answer I want to know I don't know but I might be putting the answer I want to know number but I might 3/4 6/4 I don't know but not 3/4 6/4 I don't know but not 9/4 but I do I don't know but I might 6/4 Yes, what do you want me to do that I want?
commutative property Mom 4 minus 3 and Adam? 4 minus 3 in a day And I fall in love with a rational number 3 in the world rational number.
4 minus 3 in the one night Okay. I don't think minus 4 in there. I don't think minus 4 in a day.
Yes. 3 minus 4 is minus 1. When do people say my Right now. So you love to come eat at the possible Korea.
Not only operations of all Okay, Adam. Yes. I don't know that a plus b r b plus a bar in the lottery and I come and say my partner that I might be multiplication to possible. a b is equal to b Every month in multiple banana addition multiplication to possible subtraction division to not possible subtraction division that money in the year of dinner and serum Adam Okay.
In the bank account balance in Adam in the bank account balance down by mature and chilling love Right.
I don't know that when they say it but I don't >> I have to associate property. association association association So but association only A plus B plus C It is the better than the associate. in associate A plus B B plus C A could be tripping You know A B C could It is the matter than multiplication.
Okay.
I don't have identity.
identity What number fraction fraction fraction Nani Yeah.
number number answer zero zero Correct.
multiplication Yeah. number multiply multiplication one one So, identity element element identity One is an identity element.
You don't know what standard addition identity zero Okay.
I don't think near my okay well which means inverse inverse a number Yeah.
add identity zero add zero a number Yeah. add zero number two on the two a yard could I have a zero credit card number?
Ah, equal and opposite reaction.
minus eight cooler on the number on the number order negative sign cooler at banana Martin and a zero off I think my three and the whole number yard cooler multiple banana one credit and in the air cancel off and on in the air you have to cancel off a denominator learn about the cancel off so far yeah one by one by eight cooler one by eight cooler the multiple banana and the cancel off home so far yeah what a inverse yard and get down and off minus eight yeah what a inverse yard and get down and off one by eight one of the operation addition but ah plus a portal get down and off minus eight multiplication portal get down and off one by eight I think I got that off in distributive distribute now and off but it's a pretty pretty pretty good credit card number distributive fun get to okay what you have to be my man getting down and off and the whole multiplication B plus C getting down and off see associate you and I would um save it save it fun save it fun book fun get to fun book or with the outside >> Like this. Okay, madam.
B coordinate share for a C coordinate share for a coordinate.
A into B plus A into C.
You got it, பசங்களா?
Verify the closure property number -5/7 and 8/9 addition -5/7 8/9 LCM So 79 7 table 9th table 63 7 9s 7 into 9 which is 63 -5/7 in a matter multiple -45 by 63 8 by 9 into 8 7s are 56 divided by 63 a llama -45 and 56 add banana pudding here >> So, what is your answer? Your answer is 11 by 63.
11 by 63 is a rational number.
Okay.
So, -5/7 and you 8/9 and you multiple by near to near multiple by near to near multiple -40 / 63.
Yeah, that one. single You are a rational number or Yes, I'm a is a rational number.
I'm going to close your property and verify money actually hands close your property verified or close your property is true I mean I need to go there. Next question for a month.
I don't have questions for you to easy to come.
You can answer for another person in love. What we can answer for this one?
In the category committed to property. I don't have to buy my drum okay but I don't have to check money first addition to next multiplication to okay.
I'm minus 10 by 11 you minus 8 by 33 you first add to my You are going to go to get your same number or my I'm going to go to get your same number or my I don't have to go to get your same number or my terms. I don't have to go to get your same number or my terms I don't have to go to get your same number or my terms. This two are different. I don't have to go to get your same number I don't have to go to get your same number or my terms I don't have to go to get your same number or my terms I don't have to go to get your same number or my terms I don't have to go to get your I don't have to go to get your same number or my terms I don't have to go to get your same number or my terms I don't have to go to get your same number or my Come everyone.
I'm waiting for your reply Kamala.
33 la yes 3 Allah multiple number.
So in the minus 30 divided by 33.
First minus 30 by 33 a in the minus 8 by 33 Buddha at banana.
At banana Google.
Minus 30 minus 8.
For minus 38 by 33 in the number.
Correct ah?
It is good at it also learn next in the salon. Marty multiple banana.
See Marty at banana.
Okay.
38 and a worm.
Minus 8 by 33 minus 30 by 33 add for now.
minus 8 minus 13 and then what he got you down.
minus 38 by 33 in the answer correct answer. No, 10 by 11.
minus 8 by 33 could add banana and all the matter that would be. minus 8 by 33 minus 10 by 11 could add banana and all the matter that would be.
If we want that it could be the commutative property. Should be a multiplication back llama.
Right.
for multiplication cover 12th class goes if I am a mama rooster.
Look at the start button and I can locate. Yeah, I'm out there and I did.
minus 10 by 11 into minus 8 by 33 What I tell one and I can come.
minus into minus and I don't know what is minus into minus.
Mhm, good. Plus. plus 80 divided by 11 into 33 33 33 36 6 363 -8 by 33 you -10 by 11 you Sure. Okay.
Okay. Done. Next associative property a lot property associative property set pool Verify the associative property for for the rational numbers, okay?
Yes. -7/9 5/6 -4/3 You know what I'm saying, right? You know what I'm saying? Associative property you know what I'm saying?
So the first number in the problem is on the left-hand side.
What is -7 and 9? I think I'm going to add 5 and 6.
What is the answer? LCM What is the answer? 18 LCM or what?
18 is the LCM. You know what I'm saying?
-7/9 You know what I'm saying? Multiply into 2 into 2. -14/18 5/6 you know what I'm saying? Multiply into into 3 into 3 15/18 You know what I'm saying? You know what I'm saying? You know what I'm saying?
You know what I'm saying? You know what I'm saying? Add them together. -14/18 15/18 you know what I'm saying? You know what I'm saying? What is your answer?
1/18 You know what I'm saying?
Yes or no? 1/18 You know what I'm saying? You know what I'm saying? You know what I'm saying?
You know what I'm saying? Add them together. You know what I'm saying? You know what I'm saying? You know what I'm saying? Add them together. 1/18 you know what I'm saying?
You know what I'm saying? -4/3 you know what I'm saying? Add them together. You know what I'm saying? You know what I'm You know what I'm saying? You know You know what I'm saying? You know what Why are you multiplying adding 2 into 2?
You know what I'm saying? 2 into 2 you know what I'm saying?
You know what I'm saying? You know what I'm saying?
You know what I'm You know what I'm saying? 18 9 twos are 18 6 * 3 = 2 * 2 So 24/18 1 - 24/18 -23/18 -23/18 -7/9 5/6 -4/3 -23/18 5/6 -4/3 6 * 2 * 2 5/6 8/6 5 - 8 3/6 You are late now, Abhinaya.
>> Anna Wilson Miller Correct up.
Okay.
People minus 7 by 9 multiple burner.
Okay, that would be a chicken now.
Before one day answer to the 7 by 9 quota.
LCM in a day What is the LCM your LCM is 18? Apple Milan wall at wall a multiple burner. 3 Allah 3 Allah sorry Martha.
This is 3 and this is 2.
This is 3. This is 2.
So for minus 9 by 18 plus 14 by 18.
In a drama critical minus 9 plus 14 by 18.
Sorry, minus 7 left.
In the minus one.
Okay.
In a drama answer over there. What is your answer? Your answer is when you get away catch you. When you pick your minus 23 by 18.
Minus 23 by 18.
Correct up. Now I'm already in a bottle.
You will get ready better at when you get ready at minus 23 by 18. If I never mind that 5 by 6 CU in the minus 4 by 3 you add money down. Can I see that going to play minus 7 by 9 quota at money? I would be planning a low in a cat answer.
Mother down ready to it is all ready to pay that in a associative property.
Should you have a mom?
Got it personally.
>> into C What is A into C?
Uh minus 1 by 2 So 5 by 12 So denominator or a mother of another into into four answer So final A into B you A into C you add banana banana minus 4 by 12 5 by 12 could I add banana 1 by 12 answer I want Okay now I think So the video you next check banana full amount distributive property where you can number one circle either you can 3 3 1 1 maybe only I put it You are not a person like If I walk in love I put the rewind bunny bunny character with a If you do rewinding character with it out there, Mom.
I didn't property verify all around the Dharma. I didn't property verify the wrong way easy. And it all in there.
Why? Only -15 by 19 + 15 by 19. Yeah, I could have fun and it could be 10 by 19 below. Yeah, I could have zero could have fun now. I would have done -18 by 25 zero could have fun now. I would have -18 by 25 could have fun now. I would have done. I think it could be anything.
It could be done. I didn't property property. So you know. Yes, for addition.
You do my dream multiplication character on there. Multiplication character on there.
I don't have fun now in into one into one. One one and a multiple fun and it could be the answers could be good. I would have done simple love.
I don't have fun and I don't have anything love.
Is everyone here?
If I load up a lot of money but check money by the way.
Yeah, okay now. If I don't remember when I go to addictive and multiplicative inverse inverse now you don't know.
Minus 7 by 17. Yeah, I could have fun now zero or one.
You know the 17 is going to learn and I don't know plus seven.
Correct?
I don't know why. 17 by 27.
Yeah, I could have fun now zero or one.
Minus 17 by 27. When I come minus 11 down plus learn the value plus learn the one minus learn learn the zero or one or one. Okay, why don't know why? You need to pay the inverse.
I didn't know. You need to multiplication.
multiplication Yeah, I could have one or one or one getting in now. Minus 7 by 17.
Okay, why? Minus 7 by 17. I could have multiple fun now or one.
17 by minus 7 multiple fun I don't know what I don't know 7 7 cancel 17 17 cancel I want to learn the way. I don't know why. 17 by 27. I could have multiple fun now. 27 by 17. 17 17 cancel I 27 27 cancel out. I don't know why. I don't know when you actually I don't know why the person in a lot of >> I hope So, bye-bye everyone.
the 1.3 one mark sums the one mark sums try out Ta-da!
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